- Ordering Rounding and Order of Operations
- Home
- Introduction to Inequalities
- Comparing a Numerical Expression With a Number
- Ordering Large Numbers
- Rounding to Tens or Hundreds
- Rounding to Hundreds or Thousands
- Rounding to Thousands, Ten Thousand, or Hundred Thousand
- Estimating a Sum of Whole Numbers
- Estimating a Difference of Whole Numbers
- Estimating a Product of Whole Numbers
- Estimating a Quotient of Whole Numbers
- Writing Expressions Using Exponents
- Introduction to Exponents
- Power of 10: Positive Exponent
- Power of 10: Negative Exponent
- Introduction to Parentheses
- Comparing Numerical Expressions With Parentheses
- Introduction to Order of Operations
- Order of Operations With Whole Numbers
- Order of Operations With Whole Numbers and Grouping Symbols
- Order of Operations With Whole Numbers and Exponents: Basic

- Selected Reading
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# Power of 10: Negative Exponent

In this lesson, we deal with problems involving expressions with 10 as base having negative exponents.

**Rules to find the negative exponent of 10**

Suppose we have an expression having 10^{-n}.

In normal course the value of 10

^{-n}is found by multiplying the base

10 'n' times in the denominator and putting a 1 in the numerator.We use a shortcut to solve such problem. We look at the exponent and then write a decimal point followed by as many zeros as one less than exponent and a 1.

Evaluate 10^{-3}

### Solution

**Step 1:**

Here we have an expression involving power of ten with a negative exponent.

The base is 10 and the exponent is −3.

**Step 2:**

In normal course the value of 10^{-3} can be found by multiplying the base 10 three times in the denominator and putting a 1 in the numerator.

10^{-3} = = 0.001

**Step 3:**

Using a shortcut, we find that the exponent is -3. We write a decimal point followed by two (1 less than 3) zeros and a 1.

So 10^{-3} = 0.001

Evaluate 10^{-5}

### Solution

**Step 1:**

Here we have an expression involving power of ten with a negative exponent.

The base is 10 and the exponent is −5.

**Step 2:**

In normal course the value of 10^{-5} is found by multiplying the base 10 five times in the denominator and putting a 1 in the numerator.

10^{-5} = = 0.00001

**Step 3:**

Using a shortcut, we find the exponent is -5. We write a decimal point followed by four (1 less than 5)zeros and a 1.

So 10^{-5} = 0.00001