Let's solve the problem step by step.
The task is to write each given number in
expanded form, which means breaking down the number into its place values (ones, tenths, hundredths, thousandths, etc.).
We are given an example:
> 25.742 = 20 + 5 + 7/10 + 4/100 + 2/1000
So we'll follow the same pattern: break the number into whole number parts and fractional parts based on decimal places.
---
a) 1.5
Break it down:
- 1 = 1 (ones)
- 0.5 = 5/10 (tenths)
Answer:
1.5 = 1 + 5/10
---
b) 6.7
- 6 = 6 (ones)
- 0.7 = 7/10 (tenths)
Answer:
6.7 = 6 + 7/10
---
c) 15.9
- 15 = 10 + 5 → but better to keep as 15 (tens and ones), or break further:
- 10 (from 1 ten)
- 5 (from 5 ones)
- 0.9 = 9/10
So:
15.9 = 10 + 5 + 9/10
Answer:
15.9 = 10 + 5 + 9/10
---
d) 3.82
- 3 = 3 (ones)
- 0.8 = 8/10
- 0.02 = 2/100
Answer:
3.82 = 3 + 8/10 + 2/100
---
e) 0.47
- No whole number part
- 0.4 = 4/10
- 0.07 = 7/100
Answer:
0.47 = 4/10 + 7/100
---
f) 2.648
- 2 = 2 (ones)
- 0.6 = 6/10
- 0.04 = 4/100
- 0.008 = 8/1000
Answer:
2.648 = 2 + 6/10 + 4/100 + 8/1000
---
g) 0.500
- No whole number
- 0.5 = 5/10
- 0.00 = 0/100
- 0.000 = 0/1000
But since the zeros don't add value, we can simplify:
0.500 = 5/10
However, if we follow the full expanded form including all digits:
0.500 = 5/10 + 0/100 + 0/1000
But usually, we only include non-zero parts unless specified otherwise.
But since the example includes all digits (e.g., 25.742 includes all), let’s include all:
Answer:
0.500 = 5/10 + 0/100 + 0/1000
Alternatively, simplified:
0.500 = 5/10
But for consistency with the example, let’s write it fully:
Answer:
0.500 = 5/10 + 0/100 + 0/1000
---
h) 40.031
- 40 = 40 (forty)
- 0.03 = 3/100
- 0.001 = 1/1000
Break 40 into tens and ones:
40 = 40 (or 4 tens + 0 ones)
So:
40.031 = 40 + 0/10 + 3/100 + 1/1000
Or more clearly:
= 40 + 3/100 + 1/1000
Answer:
40.031 = 40 + 3/100 + 1/1000
---
i) 0.052
- 0 whole
- 0.05 = 5/100
- 0.002 = 2/1000
So:
0.052 = 5/100 + 2/1000
Answer:
0.052 = 5/100 + 2/1000
---
j) 3.440
- 3 = 3 (ones)
- 0.4 = 4/10
- 0.04 = 4/100
- 0.000 = 0/1000
So:
3.440 = 3 + 4/10 + 4/100 + 0/1000
But again, trailing zero may be omitted. But since the number is written as 3.440, it implies precision to thousandths.
So include all:
Answer:
3.440 = 3 + 4/10 + 4/100 + 0/1000
---
Final Answers:
a) 1.5 =
1 + 5/10
b) 6.7 =
6 + 7/10
c) 15.9 =
10 + 5 + 9/10
d) 3.82 =
3 + 8/10 + 2/100
e) 0.47 =
4/10 + 7/100
f) 2.648 =
2 + 6/10 + 4/100 + 8/1000
g) 0.500 =
5/10 + 0/100 + 0/1000
h) 40.031 =
40 + 3/100 + 1/1000
i) 0.052 =
5/100 + 2/1000
j) 3.440 =
3 + 4/10 + 4/100 + 0/1000
✔ These match the format shown in the example.
Parent Tip: Review the logic above to help your child master the concept of expanded notation with decimals worksheet.
