Adding & subtracting decimal numbers
🎯 In this topic you will
- Compose, decompose, and regroup decimals with up to three decimal places.
- Estimate, add, and subtract numbers with the same or different numbers of decimal places.
🧠 Key Words
- decimal place
- trailing zero
Show Definitions
- decimal place: The position of a digit to the right of the decimal point that shows its value in tenths, hundredths, thousandths, and so on.
- trailing zero: A zero written at the end of a decimal number that does not change the value but can show the level of precision.
🏃 Comparing Race Times
Usain Bolt broke the world record for the 100 metres in 2009 by running it in 9.58 seconds. The qualifying time for the 2020 Olympics is 10.05 seconds. To find the difference between these two times, you need to subtract. In this section, you will learn more about adding and subtracting decimals.
❓ EXERCISES
1. Which of the following is equivalent to $6.075$?
a. $6 + 0.7 + 0.5$
b. $6 + 0.7 + 0.05$
c. $6 + 0.07 + 0.05$
d. $6 + 0.07 + 0.005$
👀 Show answer
2. Write the missing numbers.
$37.844 = 30 + 7 + \square + 0.04 + \square$
👀 Show answer
3. Which two numbers have a total of $1$?
$0.80,\ 0.08,\ 0.88,\ 0.02,\ 0.12,\ 0.22$
👀 Show answer
$0.80 + 0.20$ (not present),
$0.88 + 0.12 = 1$,
$0.80 + 0.20$ not available,
$0.78$ etc.
From the list: $0.88$ and $0.12$.
4. Find the sum of all the numbers less than $5.5$ in this list.
$5.05,\ 5.55,\ 5.115,\ 5.5,\ 5.555$
👀 Show answer
Sum $= 5.05 + 5.115 = 10.165$.
5. Complete these calculations.
a. $14.8 + 5.678$
b. $13.26 + 17.604$
c. $45.83 + 31.104$
d. $56.1 - 26.64$
e. $68.603 - 52.75$
f. $70.394 - 49.78$
👀 Show answer
b. $30.864$
c. $76.934$
d. $29.46$
e. $15.853$
f. $20.614$
6. Ahmed calculates: $0.7 + 0.41 = 0.48$
He has made a mistake. How can you help him avoid making the same mistake again?
👀 Show answer
Correct sum: $0.70 + 0.41 = 1.11$.
7. Calculate $1.4 + 2.56 - 3.789$
👀 Show answer
$3.96 - 3.789 = 0.171$.
8. Mike and Long dig up potatoes.
Mike digs up $8.45$ kilograms of potatoes.
Long digs up $10.5$ kilograms of potatoes.
How many kilograms of potatoes do they dig up altogether?
👀 Show answer
9. Some children are collecting money for a charity.
Their target is $350$ dollars. They have collected $158.73$ dollars so far.
How much more money do they need to reach their target?
👀 Show answer
10. Darius packs two suitcases to take on a plane.
One suitcase weighs $11.284$ kg. The other weighs $8.65$ kg.
Darius is allowed to take $20$ kg of luggage on the plane.
How much are his suitcases under the $20$ kg limit?
👀 Show answer
Under limit $= 20 - 19.934 = 0.066$ kg.
🧠 Think like a mathematician
Arrange the digits $0, 1, 2, 3, 4, 5, 6$ and $7$ to make two numbers with $3$ decimal places.
- Find the sum closest to $4$.
- Find the difference closest to $1$.
👀 show answer
Sum close to $4$: $1.673 + 2.405 = 4.078$ (very close to $4$).
Difference close to $1$: $3.752 - 2.641 = 1.111$ (close to $1$).
Many answers are possible as long as each digit $0$–$7$ is used once in each pair.