Problem 49 Convert to standard notation. ... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 6: Problem 49

Convert to standard notation. $$ 42.7 \text { million } $$

Short Answer

Expert verified

42,700,000

Step by step solution

Understand the Meaning of 'Million'

A million is represented by the number 1 followed by six zeros: $1,000,000$. This is important for converting the given value from verbal to numerical form.

Write the Number in Numeric Form

Since 'million' means $1,000,000$, the given number $42.7$ million can be expressed as $42.7 \times 1,000,000$.

Perform the Multiplication

$42.7 \times 1,000,000 = 42,700,000$. This multiplication shifts the decimal point 6 places to the right.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number conversion

Number conversion involves changing a number from one form to another. In this exercise, we are converting a verbal form of the number into standard notation. '42.7 million' is a verbal description, which tells us how many units of a million there are. To convert this to standard notation, we first need to understand what 'million' means in numerical terms. A million is represented as 1,000,000. Therefore, '42.7 million' means we have 42.7 units of one million.

multiplication

Multiplication helps us convert the number from its verbal form to numeric form. When we multiply 42.7 by 1,000,000, we effectively move the decimal point 6 places to the right because there are six zeros in 1,000,000. This is why we get 42,700,000 as our final result. Multiplication by powers of 10 like this is a powerful tool to convert between different forms of a number quickly and accurately. In summary:

Original number: 42.7
Multiplier: 1,000,000
Result: 42,700,000

place value

Place value is the numerical value that a digit has based on its position in a number. In any number, each digit has a different place value. For example, in the number 42,700,000:

The 4 is in the ten-million place.
The 2 is in the million place.
The 7 is in the hundred-thousand place.
The other zeros fill the remaining place values, indicating no additional units there.

When converting '42.7 million' to standard notation, understanding place value is crucial because we move the decimal point six places to the right, filling in any gaps with zeros as required.

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91影视

Convert to standard notation. $$ 42.7 \text { million } $$

Short Answer

Step by step solution

Understand the Meaning of 'Million'

Write the Number in Numeric Form

Perform the Multiplication

Key Concepts

number conversion

multiplication

place value

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