Here are the step-by-step solutions for each problem on the worksheet. Remember the main rule: when adding or subtracting, your final answer must be rounded to the same number of
decimal places as the number in the problem with the *fewest* decimal places.
1. $1.35 \text{ m} + 2.627 \text{ m}$
* $1.35$ has
2 decimal places.
* $2.627$ has
3 decimal places.
* The least precise number is $1.35$ (2 decimal places), so we round our answer to 2 decimal places.
* Calculation: $1.35 + 2.627 = 3.977$
* Rounding $3.977$ to two decimal places gives us $3.98$.
2. $1.005 \text{ mL} - 42 \text{ mL}$
* $1.005$ has
3 decimal places.
* $42$ has
0 decimal places (it is a whole number).
* The least precise number is $42$ (0 decimal places), so we round our answer to the nearest whole number.
* Calculation: $1.005 - 42 = -40.995$
* Rounding $-40.995$ to the nearest whole number gives us $-41$.
3. $12.01 \text{ mL} + 3.52 \text{ mL} + 5 \text{ mL}$
* $12.01$ has
2 decimal places.
* $3.52$ has
2 decimal places.
* $5$ has
0 decimal places.
* The least precise number is $5$ (0 decimal places), so we round to the nearest whole number.
* Calculation: $12.01 + 3.52 + 5 = 20.53$
* Rounding $20.53$ to the nearest whole number gives us $21$.
4. $65.46 \text{ g} - 23.7 \text{ g}$
* $65.46$ has
2 decimal places.
* $23.7$ has
1 decimal place.
* The least precise number is $23.7$ (1 decimal place), so we round to 1 decimal place.
* Calculation: $65.46 - 23.7 = 41.76$
* Rounding $41.76$ to one decimal place gives us $41.8$.
5. $501 \text{ cm} + 2.25 \text{ cm} + 100.1 \text{ cm}$
* $501$ has
0 decimal places.
* $2.25$ has
2 decimal places.
* $100.1$ has
1 decimal place.
* The least precise number is $501$ (0 decimal places), so we round to the nearest whole number.
* Calculation: $501 + 2.25 + 100.1 = 603.35$
* Rounding $603.35$ to the nearest whole number gives us $603$.
6. $0.15 \text{ cm} + 1.15 \text{ cm} + 2.051 \text{ cm}$
* $0.15$ has
2 decimal places.
* $1.15$ has
2 decimal places.
* $2.051$ has
3 decimal places.
* The least precise numbers have 2 decimal places, so we round to 2 decimal places.
* Calculation: $0.15 + 1.15 + 2.051 = 3.351$
* Rounding $3.351$ to two decimal places gives us $3.35$.
7. $110.17 \text{ L} + 4 \text{ L}$
* $110.17$ has
2 decimal places.
* $4$ has
0 decimal places.
* The least precise number is $4$ (0 decimal places), so we round to the nearest whole number.
* Calculation: $110.17 + 4 = 114.17$
* Rounding $114.17$ to the nearest whole number gives us $114$.
8. $505 \text{ kg} - 40.025 \text{ kg}$
* $505$ has
0 decimal places.
* $40.025$ has
3 decimal places.
* The least precise number is $505$ (0 decimal places), so we round to the nearest whole number.
* Calculation: $505 - 40.025 = 464.975$
* Rounding $464.975$ to the nearest whole number gives us $465$.
9. $1.202 \text{ mm} + 0.115 \text{ mm} + 0.012 \text{ mm}$
* $1.202$ has
3 decimal places.
* $0.115$ has
3 decimal places.
* $0.012$ has
3 decimal places.
* All numbers have 3 decimal places, so we keep 3 decimal places in the answer.
* Calculation: $1.202 + 0.115 + 0.012 = 1.329$
* The answer is already at 3 decimal places: $1.329$.
10. $1.218 \times 10^2 \text{ m} + 1.4567 \times 10^2 \text{ m}$
* First, convert from scientific notation to standard form to see the decimal places clearly.
* $1.218 \times 10^2 = 121.8$ (
1 decimal place)
* $1.4567 \times 10^2 = 145.67$ (
2 decimal places)
* The least precise number is $121.8$ (1 decimal place), so we round to 1 decimal place.
* Calculation: $121.8 + 145.67 = 267.47$
* Rounding $267.47$ to one decimal place gives us $267.5$.
* *(Note: You can also write this back in scientific notation as $2.675 \times 10^2 \text{ m}$)*
Final Answer:
1. 3.98 m
2. -41 mL
3. 21 mL
4. 41.8 g
5. 603 cm
6. 3.35 cm
7. 114 L
8. 465 kg
9. 1.329 mm
10. 267.5 m (or $2.675 \times 10^2$ m)
Parent Tip: Review the logic above to help your child master the concept of significant digits worksheet.
