Arithmetic

Select all the numbers that have a value of 38.5 when rounded to the nearest tenth. A) 38.518 B) 38.464 C) 38.553 D) 38.417 E) 38.507

Step-by-step solution with explanation

Final Answer

A) 38.518, B) 38.464, and E) 38.507 all round to 38.5. Options C and D do not.

Step-by-step solution

Understand rounding to nearest tenth

The tenths place is the first digit after the decimal point. To round to the nearest tenth, we look at the hundredths digit (the second digit after the decimal) to decide whether to round up or keep the tenths digit the same.

State the rounding rule clearly

If the hundredths digit is 5 or more, add 1 to the tenths digit. If it is 4 or less, leave the tenths digit alone. We need the result to equal 38.5.

Check option A: 38.518

The hundredths digit is 1, so we round down and keep the tenths digit as 5. Result is 38.5. Option A works.

Check option B: 38.464

The tenths digit is 4 and the hundredths digit is 6, so we round up: 4 becomes 5. Result is 38.5. Option B works.

Check option C: 38.553

The hundredths digit is 5, so we round up the tenths digit: 5 becomes 6. Result is 38.6, not 38.5. Option C does NOT work.

Check option D: 38.417

The tenths digit is 4 and the hundredths digit is 1, so we round down and keep 4. Result is 38.4, not 38.5. Option D does NOT work.

Check option E: 38.507

The hundredths digit is 0, so we round down and keep the tenths digit as 5. Result is 38.5. Option E works.

Understanding this problem

Learning Insight

Rounding works by finding the closest value at the desired place. Any number from 38.450 up to (but not including) 38.550 rounds to 38.5, because those numbers are closer to 38.5 than to 38.4 or 38.6. Think of it as a number line with 38.5 in the middle.

Quick Tip

Just check the single digit directly to the RIGHT of the place you are rounding to. That one digit tells you everything — ignore all digits beyond it.

Common Mistake

Students often look at ALL the digits after the tenths place instead of just the hundredths digit. For example, they might think 38.464 stays at 38.4 because '64 is not big,' but only the 6 in the hundredths place matters.