Solution - Long subtraction
Step-by-step explanation
1. Rewrite the numbers from top to bottom, aligned by their place values
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 1 | 3 | . | 4 | 5 | 1 | |||
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . |
Put zeros in the blank number places:
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . |
2. Subtract the numbers using long subtraction method
Because the upper digit (0) in the hundred thousandths column is too small to get a positive difference, borrow 1 from the number to the left (10) which becomes (09) and get (10).
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . |
Subtract the numbers in the hundred thousandths column from the top number:
10-0-9=1
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 1 |
Subtract the numbers in the ten thousandths column from the top number:
9-2=7
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 7 | 1 |
Because the upper digit (0) in the thousandths column is too small to get a positive difference, borrow 1 from the digit (5) in the next number place which becomes (4) and get (10).
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 7 | 1 |
Subtract the numbers in the thousandths column from the top number:
10-3=7
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 7 | 7 | 1 |
Because the upper digit (4) in the hundredths column is too small to get a positive difference, borrow 1 from the digit (4) in the next number place which becomes (3) and get (14).
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 7 | 7 | 1 |
Subtract the numbers in the hundredths column from the top number:
14-5=9
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 9 | 7 | 7 | 1 |
Subtract the numbers in the tenths column from the top number:
3-2=1
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 1 | 9 | 7 | 7 | 1 |
Because the upper digit (3) in the ones column is too small to get a positive difference, borrow 1 from the digit (1) in the next number place which becomes (0) and get (13).
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 13 | |||||||
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| . | 1 | 9 | 7 | 7 | 1 |
Subtract the numbers in the ones column from the top number:
13-5=8
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 13 | |||||||
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| 8 | . | 1 | 9 | 7 | 7 | 1 |
Write 0 in the tens place.
| Place value | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | 13 | |||||||
| 3 | 14 | |||||||
| 4 | 10 | |||||||
| 0 | 9 | 10 | ||||||
| 1 | 3 | . | 4 | 5 | 1 | 0 | 0 | |
| - | 5 | . | 2 | 5 | 3 | 2 | 9 | |
| 0 | 8 | . | 1 | 9 | 7 | 7 | 1 |
The solution is: 8.19771
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