Problem 29 Write decimal notation. $$ \... [FREE SOLUTION]

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Basic College Mathematics

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

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 4: Problem 29

Write decimal notation. $$ \frac{78}{10,000} $$

Short Answer

Expert verified

0.0078

Step by step solution

Understand the Fraction

The fraction $\frac{78}{10,000}$ represents the division of 78 by 10,000. To convert this to a decimal, you need to divide the numerator by the denominator.

Perform the Division

Carry out the division operation 78 梅 10,000. A simple way to do this is to move the decimal point in 78 four places to the left because 10,000 has four zeros.

Move the Decimal Point

Starting with 78, move the decimal point four places to the left. Since 78 can be written as 78.0000, moving the decimal four places to the left gives you 0.0078.

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Key Concepts

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

Fraction to Decimal Conversion

A fraction represents a part of a whole. In mathematical terms, the fraction $\frac{78}{10,000}$ shows how many parts you have out of a total. To convert a fraction into a decimal, you divide the numerator (the top number) by the denominator (the bottom number). This operation effectively transforms the fraction into a value between whole numbers, making it easier to work with in calculations and daily life. Converting the fraction $\frac{78}{10,000}$ means dividing 78 by 10,000. The resulting decimal is a more straightforward way to express the fraction numerically.

Moving Decimal Points

Moving the decimal point is a handy trick for quickly performing division by powers of ten, such as 10, 100, 1,000, or 10,000. In our example, to convert $\frac{78}{10,000}$, observe that 10,000 is a power of ten with four zeros. This means you can move the decimal point in your number four places to the left.
Since 78 is a whole number, think of it as 78.0000. Moving the decimal four places left turns 78.0000 into 0.0078. By shifting the decimal, you simplify the operation without cumbersome long division. Remember, the number of zeros in the denominator dictates the number of decimal places you move.

Division by Powers of Ten

Dividing by powers of ten is straightforward once you understand the role of zeros. Powers of ten consist of numbers like 10 (10^1), 100 (10^2), 1,000 (10^3), and so forth. Each zero in these numbers indicates how many places to move the decimal point.
For example, dividing a number by 10 means moving the decimal one place to the left. Dividing by 100 moves it two places, and by 10,000, four places. Using this knowledge, dividing 78 by 10,000 involves shifting the decimal point from 78.0000 to 0.0078. This simple method allows quick and easy calculations, ensuring accuracy in converting fractions to decimals.

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91影视

Write decimal notation. $$ \frac{78}{10,000} $$

Short Answer

Step by step solution

Understand the Fraction

Perform the Division

Move the Decimal Point

Key Concepts

Fraction to Decimal Conversion

Moving Decimal Points

Division by Powers of Ten

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