Q1.
Write the detailed place value computation for 84.691 – 77.345, and its compact form.
Answer
Detailed place value form
84.691 = 8 × 10 + 4 × 1 + 6 × 1⁄10 + 9 × 1⁄100 + 1 × 1⁄1000
77.345 = 7 × 10 + 7 × 1 + 3 × 1⁄10 + 4 × 1⁄100 + 5 × 1⁄1000
Thousandths: 1 – 5 → borrow 1 hundredth
9 hundredths → 8 hundredths, thousandths become 11
11 – 5 = 6 thousandths
Hundredths: 8 – 4 = 4 hundredths
Tenths: 6 – 3 = 3 tenths
Ones: 4 – 7 → borrow 1 ten
8 tens → 7 tens, ones become 14
14 – 7 = 7 ones
Tens: 7 – 7 = 0 tens
= 0 × 10 + 7 × 1 + 3 × 1⁄10 + 4 × 1⁄100 + 6 × 1⁄1000
77.345 = 7 × 10 + 7 × 1 + 3 × 1⁄10 + 4 × 1⁄100 + 5 × 1⁄1000
Thousandths: 1 – 5 → borrow 1 hundredth
9 hundredths → 8 hundredths, thousandths become 11
11 – 5 = 6 thousandths
Hundredths: 8 – 4 = 4 hundredths
Tenths: 6 – 3 = 3 tenths
Ones: 4 – 7 → borrow 1 ten
8 tens → 7 tens, ones become 14
14 – 7 = 7 ones
Tens: 7 – 7 = 0 tens
= 0 × 10 + 7 × 1 + 3 × 1⁄10 + 4 × 1⁄100 + 6 × 1⁄1000
Compact form
84.691
– 77.345
= 7.346
– 77.345
= 7.346
Why it happens: only two borrowings are needed — one from the hundredths into the thousandths, and one from the tens into the ones. The tenths and hundredths columns subtract without any trouble.
Check it yourself: 7.346 + 77.345 = 84.691 ✓