Chapter 5 of 6

All 6 chapters
  1. 1Hundreds, tens and ones, readunderstood
  2. 2Thousands, readunderstood
  3. 3Counting on in big steps, readunderstood
  4. 4Comparing and ordering, readunderstood
  5. 5Rounding and estimating, readunderstood
  6. 6Up to a million, and lakhs, readunderstood

M2.1.5 Chapter 5

Rounding and estimating

A sack has 3 472 seeds. Why do people say about 3 500?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Round a number to the nearest 10, 100 or 1 000
  • Estimate the seeds in a sack by counting one cupful

A sack holds 3 472 seeds. Mei says there are about 3 500. Is Mei wrong?

We round a number to make it quicker to use. The new number is close to the old one.

You round to the nearest 10, 100 or 1 000. Let us round 3 472 to the nearest 100.

Draw it first

Round 3 472 to the nearest 100

  1. A number line from 3 400 to 3 500 with the middle marked. The labels are 3 400, 3 450 and 3 500. Step 2 puts a dot at 3 472 and the label 3 472. Step 3 shows two lengths under the line: 72 away from 3 400, and 28 away from 3 500.3 4003 4503 500

    1 Draw a line from 3 400 to 3 500. Mark the middle, 3 450.

  2. A number line from 3 400 to 3 500 with the middle marked. The labels are 3 400, 3 450 and 3 500. Step 2 puts a dot at 3 472 and the label 3 472. Step 3 shows two lengths under the line: 72 away from 3 400, and 28 away from 3 500.3 4003 4503 5003 472

    2 Put a dot at 3 472. It is past the middle.

  3. A number line from 3 400 to 3 500 with the middle marked. The labels are 3 400, 3 450 and 3 500. Step 2 puts a dot at 3 472 and the label 3 472. Step 3 shows two lengths under the line: 72 away from 3 400, and 28 away from 3 500.3 4003 4503 5003 47272 away28 away

    3 It is 72 from 3 400 and 28 from 3 500. It is nearer to 3 500.

Nearest 100 means the closest number that ends in 00. Here, 3 400 and 3 500 are the two choices.

There is a quick rule. Look at the digit one place to the right.

If it is 5 or more, round up. If it is 4 or less, round down.

A number halfway between two choices rounds up. 35 to the nearest 10 is 40. 250 to the nearest 100 is 300. 4 500 to the nearest 1 000 is 5 000.

A number line from 30 to 40. A dot marks 35, which is halfway. A hop goes from 35 to 40 with the label round up. The labels are the numbers 30 to 40 and round up.3031323334353637383940round up
35 is halfway between 30 and 40. Halfway rounds up.

Worked example

Round 3 472 to the nearest 10, 100 and 1 000.

  1. Nearest 10: look at the ones digit, 2. It is 4 or less, so round down. 3 470.
  2. Nearest 100: look at the tens digit, 7. It is 5 or more, so round up. 3 500.
  3. Nearest 1 000: look at the hundreds digit, 4. Round down. 3 000.

Answer: 3 470, 3 500, 3 000

A place value chart showing 3 472 under the headings thousands, hundreds, tens and ones. Under it are three lines: to the nearest 10: 3 470, to the nearest 100: 3 500, and to the nearest 1 000: 3 000.thousandshundredstensones3472to the nearest 10: 3 470to the nearest 100: 3 500to the nearest 1 000: 3 000
One number, three roundings. The place you round to changes the answer.

Look at one digit only. Do not round in two steps.

Take 8 449 to the nearest 1 000. The hundreds digit is 4, so it is 8 000. Do not go 8 449, 8 450, 8 500, 9 000. That rounds three times.

Take care with 9s. Round 9 960 to the nearest 100.

Worked example

Round 9 960 to the nearest 100.

  1. The two choices are 9 900 and 10 000.
  2. The tens digit is 6, so round up.
  3. 9 960 is 40 from 10 000 and 60 from 9 900. It is nearer to 10 000.

Answer: 10 000

See it three ways

With things

Put 17 beans in a heap. Make a group of 10. Count what is left. Is it more than half a ten?

As a picture

A number line from 10 to 20 with a dot at 17. A hop goes from 17 to 20 with the label 3 steps. The labels are the numbers 10 to 20 and 3 steps.10111213141516171819203 steps

In symbols

17 is 3 from 20 and 7 from 10. It is nearer to 20. So 17 rounds to 20.

Now think of a big sack of seeds. You cannot count every seed.

You can estimate. An estimate is a careful guess. It is close to the real number.

Count the seeds in one cupful. Then count how many cups fill the sack.

Ten small boxes in a row, standing for ten cups. Above them is the label one cup: about 300 seeds. Below them is the label 10 cups: 10 × 300 = 3 000.one cup: about 300 seeds10 cups: 10 × 300 = 3 000
Ten cups of about 300 seeds each. The sack holds about 3 000 seeds.

Worked example

A cup holds about 300 seeds. The sack fills 10 cups. About how many seeds?

  1. There are 10 cups. Each holds about 300 seeds.
  2. Multiply: 10 × 300.
  3. Times 10 puts a zero on the end. 300 becomes 3 000.

Answer: about 3 000 seeds

The sack does not hold exactly 3 000 seeds. It holds about 3 000. Saying about is right.

Try it

Estimate the beans in a bowl

You need: a small cup or tin, a bowl of dry beans or small stones, paper and a pencil.

Be safe: Do not taste or eat the beans. Keep them away from small children.

  1. Fill the small cup with beans. Level the top.
  2. Tip the cup out. Count the beans in tens. Write the number.
  3. Scoop the beans from the bowl, cup by cup. Count the cups.
  4. Multiply: cups × beans in one cup. This is your estimate.
  5. Now count all the beans in tens. How close were you?

What you will see: Your estimate is close, but not exact. Each cup holds a few more or fewer. Saying about is right.

If you cannot try it, this is what happens.
Five small boxes in a row, standing for five cups. Above them is the label one cup: 40 beans. Below them is the label 5 cups: 5 × 40 = 200.one cup: 40 beans5 cups: 5 × 40 = 200

A wrong idea many people have

To round 3 472 to the nearest 100, look at the 4. It is small, so go down to 3 400.

Why it feels right: The 4 is in the hundreds place. It seems to be the digit that decides.

The test that breaks it: Count from 3 472 up to 3 500. That is 28 steps. Count down to 3 400. That is 72 steps. 3 500 is much nearer.

What is true: Look at the digit one place to the right. Here it is the 7 in the tens place. It is 5 or more, so round up to 3 500.

Key words

round
to swap a number for a close one, quicker to use.
estimate
a careful guess, close to the real number.
halfway
in the middle of two numbers. Halfway rounds up.

Back to your guess

The answer is B: They changed it to a close number that is quicker to use.

3 500 is close to 3 472 and quicker to use. Rounding gives a close number. Saying about is right, not wrong.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Round 4 638 to the nearest 10.

    See the answer

    4 640

    Look at the ones digit, 8. It is 5 or more, so round up. 4 638 becomes 4 640.

  2. Round 5 740 to the nearest 100.

    A place value chart with four columns: thousands, hundreds, tens and ones. The digits are 5, 7, 4 and 0.thousandshundredstensones5740
    Tap your answer.

    1. Yes, that is right. The tens digit is 4. It is 4 or less, so round down. 5 740 becomes 5 700.

    2. Not this one. You may have looked at the 7 in the hundreds place. Look one place to the right, at the tens digit, 4. Try another.

    3. Not this one. That sets every digit after the 5 to 0. Look at the tens digit instead. Try another.

    See the answer

    5 700

    The tens digit is 4. It is 4 or less, so round down. 5 740 becomes 5 700.

    • If you chose B: You may have looked at the 7 in the hundreds place. Look one place to the right, at the tens digit, 4.
    • If you chose C: That sets every digit after the 5 to 0. Look at the tens digit instead.

  3. Round 250 to the nearest 100.

    Tap your answer.

    1. Not this one. It is true that 250 is the same distance from both. We agree halfway rounds up, so everyone gets the same answer. Try another.

    2. Not this one. Halfway rounds up. 250 is as near 200 as it is 300. Try another.

    3. Yes, that is right. 250 is halfway between 200 and 300. Halfway rounds up.

    See the answer

    300

    250 is halfway between 200 and 300. Halfway rounds up.

    • If you chose A: It is true that 250 is the same distance from both. We agree halfway rounds up, so everyone gets the same answer.
    • If you chose B: Halfway rounds up. 250 is as near 200 as it is 300.

  4. Round 9 960 to the nearest 100.

    See the answer

    10 000

    The tens digit is 6, so round up. 9 960 is 40 from 10 000 and 60 from 9 900.

  5. A cup holds about 20 beans. A tin takes 8 cups. About how many beans fill the tin?

    See the answer

    about 160 beans

    8 × 20 means eight 20s. 8 × 2 = 16, so 8 × 20 = 160.

  6. From an earlier chapter

    Which sign goes in the gap? 5 031 __ 987

    Tap your answer.

    1. Yes, that is right. 5 031 has four digits and 987 has three. More digits means a bigger number.

    2. Not this one. 5 031 has four digits and 987 has three. The number with more digits is bigger. Go to M2.1.4. Try another.

    3. Not this one. The numbers are not the same. 5 031 has four digits and 987 has three. Go to M2.1.4. Try another.

    See the answer

    >

    5 031 has four digits and 987 has three. More digits means a bigger number.

    • If you chose B: 5 031 has four digits and 987 has three. The number with more digits is bigger. Go to M2.1.4.
    • If you chose C: The numbers are not the same. 5 031 has four digits and 987 has three. Go to M2.1.4.

  7. Round 648 to the nearest 10.

    A place value chart with three columns: hundreds, tens and ones. The digits are 6, 4 and 8.hundredstensones648
    Tap your answer.

    1. Not this one. You looked at the 4 in the tens place. Look one place to the right, at the ones digit, 8. Try another.

    2. Yes, that is right. The ones digit is 8. It is 5 or more, so round up. 648 becomes 650.

    3. Not this one. That is rounding to the nearest 100. To the nearest 10, 648 is 640 or 650. Look at the ones digit. Try another.

    See the answer

    650

    The ones digit is 8. It is 5 or more, so round up. 648 becomes 650.

    • If you chose A: You looked at the 4 in the tens place. Look one place to the right, at the ones digit, 8.
    • If you chose C: That is rounding to the nearest 100. To the nearest 10, 648 is 640 or 650. Look at the ones digit.

  8. Round 8 970 to the nearest 100.

    Tap your answer.

    1. Not this one. You cut off the tens. The tens digit is 7, so round up. Try another.

    2. Yes, that is right. The tens digit is 7, so round up. 8 970 is 30 from 9 000 and 70 from 8 900.

    3. Not this one. 9 hundreds and 1 more make 10 hundreds. That is one more thousand, so 8 becomes 9. Try another.

    See the answer

    9 000

    The tens digit is 7, so round up. 8 970 is 30 from 9 000 and 70 from 8 900.

    • If you chose A: You cut off the tens. The tens digit is 7, so round up.
    • If you chose C: 9 hundreds and 1 more make 10 hundreds. That is one more thousand, so 8 becomes 9.

  9. Round 6 499 to the nearest 1 000.

    Tap your answer.

    1. Yes, that is right. The hundreds digit is 4. It is 4 or less, so round down. 6 499 becomes 6 000.

    2. Not this one. You rounded 499 up to 500 first. Look at one digit only, the hundreds digit, 4. Try another.

    3. Not this one. That is rounding to the nearest 100. Nearest 1 000 ends in 000. Try another.

    See the answer

    6 000

    The hundreds digit is 4. It is 4 or less, so round down. 6 499 becomes 6 000.

    • If you chose B: You rounded 499 up to 500 first. Look at one digit only, the hundreds digit, 4.
    • If you chose C: That is rounding to the nearest 100. Nearest 1 000 ends in 000.

  10. A cup holds about 40 beans. A bowl takes 9 cups. About how many beans?

    Nine small boxes in a row, standing for nine cups. Above them is the label one cup: about 40 beans. Below them is the label 9 cups.one cup: about 40 beans9 cups
    Tap your answer.

    1. Not this one. You added 40 and 9. The bowl holds 9 cups of 40 beans, so multiply. Try another.

    2. Yes, that is right. 9 × 40 means nine 40s. 9 × 4 = 36, so 9 × 40 = 360.

    3. Not this one. 9 × 4 = 36, so 9 × 40 = 360. 3 600 has one zero too many. Try another.

    See the answer

    about 360 beans

    9 × 40 means nine 40s. 9 × 4 = 36, so 9 × 40 = 360.

    • If you chose A: You added 40 and 9. The bowl holds 9 cups of 40 beans, so multiply.
    • If you chose C: 9 × 4 = 36, so 9 × 40 = 360. 3 600 has one zero too many.

  11. Mei counts 52 seeds in one cup. The sack fills 10 cups. What can she say?

    Tap your answer.

    1. Yes, that is right. 10 × 52 = 520. Cups are not all the same, so 520 is an estimate. Say about.

    2. Not this one. Each cup holds a few more or fewer seeds. So 520 is a careful guess, not an exact count. Try another.

    3. Not this one. You added 10 and 52. The sack holds 10 cups of 52 seeds, so multiply. Try another.

    See the answer

    There are about 520 seeds.

    10 × 52 = 520. Cups are not all the same, so 520 is an estimate. Say about.

    • If you chose B: Each cup holds a few more or fewer seeds. So 520 is a careful guess, not an exact count.
    • If you chose C: You added 10 and 52. The sack holds 10 cups of 52 seeds, so multiply.

Keep it

Copy this into your exercise book.

Look at the digit one place to the right. 5 or more rounds up. 4 or less rounds down. 3 472 is 3 500 to the nearest 100. An estimate is close, not exact.

Draw: A number line from 3 400 to 3 500. Mark 3 450 and a dot at 3 472.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (675 KB). It opens on any phone.