2.3.1 How Far is It?

Suppose you are planning a journey by road from Washington, DC to Richmond, Virginia. According to the map, it’s approximately 112 miles. Depending on where you start in Washington DC and where you end in Richmond, the total distance could be more or less than 112 miles.

Assume we start from Location A in south-west Washington, DC and drive to downtown Richmond, Virginia. The actual mileage is 111.6. We would round up to 112 miles, because the number after the decimal point is greater than or equal to 5 and is therefore closer to 112 than 111. By the same token, if we traveled a little further to the south of the James River in Richmond and the mileage was 112.3, we would not round up, because the number after the decimal point is less than 5 and this time is closer to 112 than 113.

The general rules for rounding are:

  • Locate the place value to be rounded.
  • Look at the next digit to the right (the next smaller place value).
  • If that digit is a 5 or greater, “round up” the previous place value digit—which means to increase it by one.
  • If that digit is a 4 or less, leave the previous place value digit unchanged.
  • Replace all digits after the place value digit with 0 but only if these are to the left of the decimal point

Here’s a couple of examples to have a look at.

We want to round the world population figure of 6.95 billion to the nearest billion. So the place value that we want to round in this case is the units as these represent the billions, which is a 6. The next number to the right of this is a 9, which is 5 or greater, so we need to round up the 6 to 7.

So 6.95 billion rounded to the nearest billion is 7 billion.

Now we want to round 1.72 to the nearest tenth (or to 1 decimal place). This means rounding  the 7 in the tenths place. To the right of this is a 2, which is less than 5, so we leave the 7 as it is.

So 1.72 rounded to the nearest tenth (or to 1 decimal place) is 1.7

Notepad symbol Activity: Rounding

Round each of the following numbers to the specified placeholder.

(a) Round 126.43 to the nearest tenth.

Hint symbol

Discussion

Remember that the tenths place is located immediately to the right of the decimal point and is the same as rounding to one decimal place, or “1 d.p.” Be sure to use the digit in the hundredths place to make your final decision.

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Answer

(a)

  • Locate the place value to be rounded—in this case, the number 4.
  • Look at the next one to the right—in this case, it’s 3.
  • 3 is less than 5, so we round down, and the answer is 126.4.

(b) Round 0.015474 to the nearest thousandth.

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Discussion

You will use the placeholder immediately to the right of the thousandths place to make your rounding decision. This is the same as rounding to 3 d.p.

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Answer

(b)

  • Locate the place value to be rounded—in this case, the number 5.
  • Look at the next one to the right—in this case, it’s 4.
  • Because 4 is less than 5, we round down, and the answer is 0.015.

(c) Round 1.5673 to 2 decimal places (2 d.p.).

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Answer

(c)

  • Locate the decimal place to the rounded—in this case the number is 6.
  • Look at the next one to the right—in this case, it’s 7.
  • Because 7 is greater than 5, we round up, and the answer is 1.57.

(d) The speed of light is 299,792.458 km/sec. Round that number to the nearest 1000 km/sec.

Hint symbol

Discussion

You will need to round to the nearest thousand (not thousandth). Be careful!

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Answer

(d)

  • Locate the place value to be rounded—it’s the second 9.
  • Look at the next one to the right—it’s 7.
  • Since 7 is more than 5, we round up. But rounding up 9 makes it 10, so we have to round up the next 9, which makes that 10 as well so we have to round up the 2 to 3.
  • So the answer is 300,000 km/sec. Notice that we write these new zeros, as they are to the left of the decimal point.

Videoclip symbolFor more exposure and practice on rounding, check out Professor Perez and see if you can get the hang of rounding and following these rules! Feel free to skip ahead in the video if you feel comfortable the material.

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2.3.2 Calculator Exploration: Decimals and Rounding