Question

practice quiz
metric conversions and significant figures: math in science

1. state the number of significant figures: 5 marks

number of significant figures:
a) 962
b) 1010
c) 500.0
d) 00.620
e) 70.90

1. state either standard notation (

egular number\) or scientific notation:
standard notation scientific notation
a) 14632
b) 0.00302
c) 7.4 x 10²
d) 16.2
e) 8.93 x 10⁻¹
f) 1.70 x 10⁻³

1. convert the following:

a) 0.2 cm to mm
b) 472 mg to g
c) 89 dm to dam
d) 31 hg to g

1. calculate the following using the correct number of significant digits:

a) 0.062 - 0.03604 =
b) 362.082 + 19.6 =
c) 79240 ÷ 0.0021060 =

Explanation:

Step1: Determine significant - figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Trailing zeros in a number with a decimal point are significant. Leading zeros are not significant.

Step2: Find significant figures for 962

All non - zero digits are significant, so 962 has 3 significant figures.

Step3: Find significant figures for 1010

Zeros between non - zero digits are significant, so 1010 has 3 significant figures.

Step4: Find significant figures for 500.0

Trailing zeros in a number with a decimal point are significant, so 500.0 has 4 significant figures.

Step5: Find significant figures for 00.620

Leading zeros are not significant, so 00.620 has 3 significant figures.

Step6: Find significant figures for 70.90

Trailing zeros in a number with a decimal point are significant, so 70.90 has 4 significant figures.

Step7: Convert to scientific notation

Scientific notation is of the form \(a\times10^{n}\), where \(1\leqslant|a|\lt10\) and \(n\) is an integer.
For 14632, it is \(1.4632\times 10^{4}\) in scientific notation.
For 0.00302, it is \(3.02\times 10^{- 3}\) in scientific notation.
For \(7.4\times 10^{2}\), the standard notation is 740.
For 16.2, it is \(1.62\times 10^{1}\) in scientific notation.
For \(8.93\times 10^{-1}\), the standard notation is 0.893.
For \(1.70\times 10^{-3}\), the standard notation is 0.00170.

Step8: Metric conversions

\(1\ cm = 10\ mm\), so \(0.2\ cm=0.2\times10 = 2\ mm\).
\(1\ g = 1000\ mg\), so \(472\ mg=\frac{472}{1000}=0.472\ g\).
\(1\ dam = 100\ dm\), so \(89\ dm=\frac{89}{100}=0.89\ dam\).
\(1\ hg = 100\ g\), so \(31\ hg = 31\times100 = 3100\ g\).

Step9: Significant - digit calculations

For \(0.062−0.03604\), \(0.062 - 0.03604=0.02596\approx0.026\) (2 significant digits as 0.062 has 2 significant digits).
For \(362.082 + 19.6\), \(362.082+19.6 = 381.682\approx381.7\) (4 significant digits as 19.6 has 3 decimal - place precision).
For \(79240\div0.0021060\), \(79240\div0.0021060=\frac{79240}{0.0021060}\approx3.7626\times 10^{7}\) (4 significant digits as 79240 has 4 significant digits).

Answer:

1.
a) 3
b) 3
c) 4
d) 3
e) 4
2.
a) Standard notation: 14632, Scientific notation: \(1.4632\times 10^{4}\)
b) Standard notation: 0.00302, Scientific notation: \(3.02\times 10^{-3}\)
c) Standard notation: 740, Scientific notation: \(7.4\times 10^{2}\)
d) Standard notation: 16.2, Scientific notation: \(1.62\times 10^{1}\)
e) Standard notation: 0.893, Scientific notation: \(8.93\times 10^{-1}\)
f) Standard notation: 0.00170, Scientific notation: \(1.70\times 10^{-3}\)
3.
a) 2 mm
b) 0.472 g
c) 0.89 dam
d) 3100 g
4.
a) 0.026
b) 381.7
c) \(3.763\times 10^{7}\)