Rounding and Decimals:

Estimate the Results of an Arithmetic Operation

When we’re in a hurry or don’t have a pen and paper, rounding can help us estimate harder arithmetic problems. This skill will help when quickly trying to see if we can afford everything on our grocery list or what this month’s budget adds up to. This is done by rounding to the highest place value we see (356 → 400 and 22.4 → 20), then addition and subtraction can be done on these rounded values much more easily. The answer we get won’t be exact, but it will be a good estimate.

Video Source (03:45 mins) | Transcript

Practice Problems

What is the result when front-end rounding is applied to the number 35,073.290?

Use rounding to estimate the solution to the problem:

26.37 + 61.72 = ?
739.6 + 479.6 = ?
6.6 − 2.5 = ?
39.225 − 13.581 = ?
3299.06 − 5323.11 = ?

Solutions

40,000 (Written Solution)

Round to the highest place value, when using front-end rounding. The number 3 has the highest place value.

35,073.290

To determine if 3 is to be rounded up or left unchanged, we look to the right of 3 at the number 5.

35,073.290

Consider the position of the number 5 in the number line. The number 5 is in the middle of 0 and 10.

Numbers 5 and greater indicate you should round up.

The number 3 will increase to 4. All the numbers to the right, become zeros.

40,000.000

The rounded answer is 40,000. (It is mathematically acceptable to drop all zeros after the decimal.)
90
- The number 26.37 rounds to 30.
- The number 61.72 rounds to 60.
- So, 26.37 + 61.72 is about equal to: 30 + 60 = 90
1200 (Solution Video | Transcript)
4
- The number 6.6 rounds to 7.
- The number 2.5 rounds to 3.
- So, 7 − 3 = 4
30
- The number 39.225 rounds to 40.
- The number 13.581 rounds to 10.
- So, 40 − 10 = 30
\(-2000\) (Solution Video | Transcript)