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Chapter 3: Problem 5

Write \(19.99\) to (a) 3 s.f., (b) 2 s.f., (c) 1 s.f.

Short Answer

Expert verified
Question: Round the number 19.99 to 1, 2, and 3 significant figures. Answer: The number 19.99 rounded to 1 significant figure is 20, to 2 significant figures is 20, and to 3 significant figures is 20.0.

Step by step solution

01

Identifying the significant figures

For the number \(19.99\), all the digits are significant figures. The significant figures, from left to right, are the \(1\), the \(9\), the \(9\), and the \(9\).
02

Rounding to 3 significant figures (3 s.f.)

To round this number to 3 significant figures, we will look at the first 3 digits and consider the 4th digit for rounding purposes. The first 3 digits are \(19.9\). Since the 4th digit (9) is greater than or equal to 5, we will round up. Rounding up, we get \(19.99 \approx 20.0\) to 3 significant figures.
03

Rounding to 2 significant figures (2 s.f.)

To round this number to 2 significant figures, we will look at the first 2 digits and consider the 3rd digit for rounding purposes. The first 2 digits are \(19\). Since the 3rd digit (9) is greater than or equal to 5, we will round up. Rounding up, we get \(19.99 \approx 20\) to 2 significant figures.
04

Rounding to 1 significant figure (1 s.f.)

To round this number to 1 significant figure, we will look at the first digit and consider the 2nd digit for rounding purposes. The first digit is \(1\). Since the 2nd digit (9) is greater than or equal to 5, we will round up. Rounding up, we get \(19.99 \approx 20\) to 1 significant figure. To summarize, the number \(19.99\) rounded to: - 3 significant figures is \(20.0\) - 2 significant figures is \(20\) - 1 significant figure is \(20\)

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Most popular questions from this chapter

To three significant figures a number is \(3.60\). State the maximum and minimum possible values of the number.

Express the following decimal numbers as proper fractions in their simplest form: (a) \(0.8\) (b) \(0.80\) (c) \(0.08\) (d) \(0.080\) (e) \(0.800\)

Express the following decimal numbers as proper fractions in their simplest form: (a) \(0.16\) b) \(0.88\) (c) \(0.108\) (d) \(0.555\) (e) \(0.965\)

Write the following fractions as decimals, giving your answer to 3 d.p.: \(\begin{array}{llll}\text { (a) } \frac{1}{3} \text { (b) } \frac{2}{3} \text { (c) } \frac{1}{9} \text { (d) } \frac{4}{11} & \text { (e) } \frac{6}{7}\end{array}\)

Write each of the following as a decimal number: \(\begin{array}{lll}\text { (a) } \frac{1}{5} \text { (b) } \frac{3}{20} & \text { (c) } \frac{7}{40} & \text { (d) } \frac{21}{84} \text { (e) } \frac{110}{20}\end{array}\)
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