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Chapter 5: Problem 29

Write each number without exponents. $$ 1 \times 10^{12} $$

Short Answer

Expert verified
1,000,000,000,000

Step by step solution

01

Understand the Exponent

The exponent in the expression is 12, which means that the number 10 is multiplied by itself 12 times.
02

Write the Number in Expanded Form

Starting from 1, move the decimal point 12 places to the right. This is equivalent to multiplying 1 by 10 twelve times.
03

Add Zeros as Placeholders

After moving the decimal point 12 places to the right, there will be 12 zeros added to the right of the 1.
04

Write the Final Number

The final number without the exponent is 1,000,000,000,000.

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Key Concepts

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

Understanding Exponents
Exponents are a fundamental part of math. They show how many times a number, known as the base, is multiplied by itself. For instance, in the expression \(10^{12}\), the number 10 is the base, and 12 is the exponent. This means \(10 \times 10 \times 10 \times \text{... (12 times)}\).
Exponents help to simplify large numbers. Instead of writing 1 followed by many zeros, we use exponents to express it clearly. Understanding how exponents work is crucial, as they are used in many areas like scientific notation and algebra.
Decimal Point Movement
When working with exponents, especially in expressions like \(1 \times 10^{12}\), we deal often with moving the decimal point. Multiplying by \(10^{12}\) means shifting the decimal point 12 places to the right.
Start with 1 (which is at 1.0), and move the decimal right by 12 spaces:
\[1.0 \rightarrow 10 \rightarrow 100 \rightarrow 1000 \rightarrow 10000 \rightarrow 100000 \rightarrow 1000000 \rightarrow 10000000 \rightarrow 100000000 \rightarrow 1000000000 \rightarrow 10000000000 \rightarrow 100000000000 \rightarrow 1000000000000\].
After shifting, you add zeros to the empty spots. If there are not enough digits, zeros are filled in, making the process straightforward.
Place Value
Place value is the foundation that helps us understand the value of each digit in a number based on its position. Each place has a value ten times that of the place to its right.
For example, in the number 1,000:
  • The 1 is in the thousands place, equating to \(1 \times 1000\).
  • Each 0 represents a smaller place value (hundreds, tens, and ones).
When moving the decimal 12 places to the right as in \(1 \times 10^{12}\), we essentially shift the place values out. The 1 moves from the ones place to \(10^{12}\) place, creating 1,000,000,000,000 as the final number, with zeros filling all the positions up to that high place value. Understanding place value clarifies why and how decimals shift.

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Most popular questions from this chapter

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