Chapter 1, Problem 1.48P

a)

Interpretation Introduction

Interpretation:131000.0 should be written in scientific notation.

Concept introduction:Very small or very large numbers are written in decimal form and is called scientific form or scientific notation. It simplifies various arithmetic operations. In this notation, numbers are expressed in the form of $m\times {10}^n$ , where $m$ is a real number and $n$ is an integer.

If number is less than zero, decimal points prior to first non-zero digit are counted and one is added to it. For example, 0.003 has two zeroes before non-zero 3 so it is written as $3\times {10}^{-3}$ .

If number is greater than zero, number of digits before decimal points is counted and one is subtracted from it. For example, 320.6 has three digits before decimal point so it is written as $3.206\times {10}^2$ .

b)

Interpretation Introduction

Interpretation:0.00047 should be written in scientific notation.

Concept introduction:Very small or very large numbers are written in decimal form and is called scientific form or scientific notation. It simplifies various arithmetic operations. In this notation, numbers are expressed in the form of $m\times {10}^n$ , where $m$ is a real number and $n$ is an integer.

If number is less than zero, decimal points prior to first non-zero digit are counted and one is added to it. For example, 0.003 has two zeroes before non-zero 3 so it is written as $3\times {10}^{-3}$ .

If number is greater than zero, number of digits before decimal points is counted and one is subtracted from it. For example, 320.6 has three digits before decimal point so it is written as $3.206\times {10}^2$ .

c)

Interpretation Introduction

Interpretation:210006 should be written in scientific notation.

Concept introduction:Very small or very large numbers are written in decimal form and is called scientific form or scientific notation. It simplifies various arithmetic operations. In this notation, numbers are expressed in the form of $m\times {10}^n$ , where $m$ is a real number and $n$ is an integer.

If number is less than zero, decimal points prior to first non-zero digit are counted and one is added to it. For example, 0.003 has two zeroes before non-zero 3 so it is written as $3\times {10}^{-3}$ .

If number is greater than zero, number of digits before decimal points is counted and one is subtracted from it. For example, 320.6 has three digits before decimal point so it is written as $3.206\times {10}^2$ .

d)

Interpretation Introduction

Interpretation:2160.5 should be written in scientific notation.

Concept introduction:Very small or very large numbers are written in decimal form and is called scientific form or scientific notation. It simplifies various arithmetic operations. In this notation, numbers are expressed in the form of $m\times {10}^n$ , where $m$ is a real number and $n$ is an integer.

If number is less than zero, decimal points prior to first non-zero digit are counted and one is added to it. For example, 0.003 has two zeroes before non-zero 3 so it is written as $3\times {10}^{-3}$ .

If number is greater than zero, number of digits before decimal points is counted and one is subtracted from it. For example, 320.6 has three digits before decimal point so it is written as $3.206\times {10}^2$ .