Rounding and significant figures questions and answers

Worked solution

1. 1st s.f. is 6 (thousands); next digit 4, so round down
2. $6000$

Worked solution

1. $3.8|46$: round down to $3.8$

Worked solution

1. The first three figures are 2, 6, 8; the next digit is 1, so round down.
2. $26\,800$

Worked solution

1. The first significant figure is 7; the next digit is 3, so round down.
2. $0.07$

Worked solution

1. $0.0045|71$: next digit 7, round up
2. $0.0046$

Worked solution

1. $258|63$: round up to $259$
2. $25\,900$

Worked solution

1. $7.04|96$: next digit 9, round up
2. $7.05$

Worked solution

1. $0.09|8$: round up, so $0.10 = 0.1$

Worked solution

1. The first two figures are 3 and 4; the next digit is 5, so round up.
2. $350\,000$

Worked solution

1. The significant figures are 4, 0, 5; the next digit is 2, so round down.
2. $0.000405$

Worked solution

1. The first two figures are 9 and 0; the next digit is 7, so round up.
2. $9.1$

Worked solution

1. The first three figures are 4, 9, 9; the next digit is 6, so round up.
2. $4.99$ rounds up to $5.00$ (written with two zeros to show 3 significant figures).

Worked solution

1. $399|60$: round up, $399 \to 400$
2. $40\,000$

Worked solution

1. $2.045 \times 3.1 = 6.3395$
2. $6.33|95 \to 6.34$

Worked solution

1. $\sqrt{50} = 7.0710\ldots$
2. To 3 s.f.: $7.07$