Rounding

Compare 74 with the midpoint between 70 and 80.

Keep the tens digit and look at the units digit.

Keep the hundreds digit and use the tens digit to decide.

The hundreds digit is the deciding digit when rounding to the nearest thousand.

Look at the first digit after the decimal point.

Keep the tenths digit and use the hundredths digit to decide.

1. Keep the 6 in the tenths place. The next digit is 8, so increase the 6 to 7.
2. Answer: 4.7.

Keep the hundredths digit and look at the thousandths digit.

1. The first two decimal digits are 3 and 4. The next digit is 2, so keep them unchanged.
2. Answer: 8.34.

Count three places after the decimal point, including zeros.

1. The first three decimal digits are 0, 7 and 6. The next digit is 2.
2. Keep the first three unchanged and remove the rest: 0.076.

Find the first non-zero digit, then look at the following digit.

1. The first significant digit is 6, in the ten-thousands place. The next digit is 8, so round 6 up to 7.
2. The other four places become zeros: 70000.

The leading zeros do not count as significant figures.

1. The first two significant digits are 4 and 7. The next digit is 2, so keep 4 and 7 unchanged.
2. Keep the leading zeros to preserve place value: 0.0047.

Decimal places count after the decimal point. Significant figures count from the first non-zero digit.

Part (a)

1. Keep the hundredths digit, 8. The next digit is 6, so round that 8 up to 9.
2. Answer: 36.49.

Part (b)

1. The first two significant digits are 3 and 6. The next digit is 4, so keep 36 unchanged.
2. Remove the following decimal digits. Answer: 36.

Rounding up a 9 can carry into the previous place. The answer must show two decimal places.

1. Keep the hundredths digit 9 and look at the next digit, 6. Round up.
2. 5.29+0.01=5.30.
3. The answer must show two decimal places, so choose 5.30. Although 5.3 has the same value, it shows only one decimal place.

The fourth significant digit decides whether the first three stay the same or round up.

1. The first three significant digits are 2, 4 and 9. The next digit is 7, so increase 249 to 250.
2. The kept third digit is in the thousands place. Preserve the remaining places with zeros.
3. Answer: 250000.

Start counting significant figures at the first non-zero digit. Zeros before it do not count.

1. The first significant digit is 4 and the second is 8. The next digit is 6, so round the 8 up to 9.
2. Answer: 0.049. The value 0.05 shows only 1 significant figure and 0.0486 shows 3.

One penny is one hundredth of a pound.

1. The nearest penny means two decimal places in pounds.
2. Keep the hundredths digit 6. The next digit is 5, so increase 6 to 7.
3. Rounded price: £18.77.

Which whole numbers are nearer to 90 than to 80 or 100? A number exactly halfway rounds up.

Part (a)

1. Halfway between 80 and 90 is 85. A halfway value rounds up, so 85 rounds to 90, but 84 rounds to 80.
2. The smallest possible number is 85.

Part (b)

1. Halfway between 90 and 100 is 95, and 95 rounds up to 100.
2. So the largest whole number that rounds to 90 is 94.

For (a), use the original number. For (b), compare the digit that decides the original rounding with the digit created by the first rounding.

Part (a)

1. Keep the tenths digit, 2, and inspect the original hundredths digit, 4.
2. Since 4 is below 5, the tenths digit stays 2. The answer is 4.2.

Part (b)

1. Her first rounding changes the hundredths digit from 4 to 5.
2. That new 5 changes the decision when she rounds again. The first rounding loses information from the original value.
3. Use the original number to round directly to the requested accuracy.

Which hundredths are nearer to 3.5 than to 3.6? Remember that a 5 in the hundredths place rounds up.

1. The numbers with two decimal places that round to 3.5 are 3.45, 3.46, ..., 3.54.
2. The next one, 3.55, rounds up to 3.6, so it is not allowed.
3. The greatest possible original number is 3.54.

Add the unrounded times first, then round the total once.

1. Total before rounding: 56.46+56.46=112.92 seconds.
2. Keep the tenths digit, 9. The next digit is 2, so it stays unchanged.
3. Answer: 112.9 seconds. Rounding each lap first would give 56.5+56.5=113.0, which is not the correctly rounded total.

Find the greatest possible whole-number order count that rounds to 950, then compare it with the boxes available.

1. The whole-number order counts from 945 to 954 round to 950. The next count, 955, rounds to 960.
2. The greatest possible shortage is therefore 954-950=4 boxes.
3. The rounded report does not guarantee that 950 boxes will be enough.