To what decimal place should each answer be rounded? How many significant figures does the rounded answer have?

(a) $101 \, \text{cm} - 99.1 \, \text{cm} = 1.9 \, \text{cm}$ (unrounded)
After rounding, the answer should be reported to the \_\_\_\_\_ and thus has \_\_\_\_\_.

(b) $0.5 \, \text{atm} + 9.8 \, \text{atm} = 10.3 \, \text{atm}$ (unrounded)
After rounding, the number should be reported to the \_\_\_\_\_ and thus has \_\_\_\_\_.

Options:
- ( ones place / tenths place / hundredths place )
- ( 1 significant figure / 2 significant figures / 3 significant figures )

When adding or subtracting quantities, the final result must be rounded to the least number of places in the decimal part of any of the quantities in the operation.

The number 101 has zero decimals while the number 99.1 has 1 decimal place, so the least number of decimals between those two quantities is 0, so the final result must contain no decimals.

In this case, 1.9 cm, which has two significant figures, must be reported with no decimals, so it must be rounded to one signficant figure, i.e. 2 cm.

After rounding, the answer should be reported to the ( ones place ) and thus has ( 1 significant figure )

(b) 0.5 atm + 9.8 atm = 10.3 atm (unrounded)

Here you are adding two quantities, so use the same rule: round to the least number of places in the decimal part of any of the quantities in the operation.

Both 0.5 atm and 9.8 atm have one decimal (tenths place), so the answer must contain one decimal too, meaning that it stands as 10.3 atm, which has three significant figures.

So, the answer is:

After rounding, the number should be reported to the ( tenths place ) and thus has ( 3 significant figure ).

adioabiola adioabiola · Answer 2 · 2025-04-26T02:09:34-04:00

The rounded off figures are as provided in the explanation below.

According to the question;

We are required to round off the values to different place values.

For Case (a);. 101 cm−99.1 cm=1.9

Ones place = 2cm
Tenths place = 1.9cm
Hundredths place = 1.90cm

For Case (b);. 0.5 atm + 9.8 atm = 10.3 atm

Ones place = 10 atm
Tenths place = 10.3 atm
Hundredths = 10.3 atm

The basis for rounding off entails that the place value immediately lower in hierarchy to the place value to be rounded to is considered;

If the digit which occupies this place value is greater or equal to 5; it is rounded to 1 and added to the required place value.

If otherwise, it is rounded to zero, 0 and added to the required digit also.