Depth · one concept from first principles · step 2 of 4

Rounding is an up or a down

Rounded to the nearest whole number, the quotient below is $4$ . Find the largest digit that $\blacksquare$ can be.

$7.\blacksquare 8 \div 1.7$

Number systemExpressionsBase-ten numbers

Your answer

How to solve

Strategy Work Backwards — Only the upper end matters, because a larger digit makes a larger dividend and so a larger quotient. So find the dividend that would push the quotient to exactly 4.5 and step back from it.

1STEP 1

Turn the rounded value back into a range

A quotient rounds to 4 exactly when it is at least 3.5 and below 4.5.

3.5 ≤ (quotient) ＜ 4.5

2STEP 2

Find the dividend at the top of the range

Multiply the upper boundary by the divisor to see how big the dividend may get.

4.5 × 1.7 = 7.65

3STEP 3

Read the largest digit that fits

With ■ = 5 the dividend is 7.58, still under 7.65; with ■ = 6 it is 7.68, which is over.

7.58 ＜ 7.65 ＜ 7.68

Answer

Divide it out: 7.58 ÷ 1.7 ≈ 4.46, which rounds to 4, while 7.68 ÷ 1.7 ≈ 4.52 rounds to 5.

Takeaway

When you want the largest digit, work from the top of the rounding range back down.

Turn the rounded value back into a range
Find the dividend at the top of the range
Read the largest digit that fits

Where next?

Another one like thissuggested

12 practice problems

Same look, different logicsuggested

Change the unit using a decimal Dividing a bigger number by a smaller one grows the quotient

Step back and solidifysuggested

Overlap of two ranges on a number line Inclusive vs exclusive range boundaries

1 reasoning problems grow out of this type — the bridge toward competition →

A parent dashboard for the family lives at sensimlab.com.

▶ Practice — 12 problems

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