Express 16.54 x 10$^{-5}$ - 6.76 x 10$^{-8}$ + 0.23 x 10$^{-6}$ in standard form

To solve this problem, we need to express all the terms in the same power of 10 so that we can easily add or subtract them.

1. Analyze the question

We are given: $16.54 \times 10^{-5} - 6.76 \times 10^{-8} + 0.23 \times 10^{-6}$

To make calculation easier, let's convert all terms to $10^{-5}$.

2. Explain the concept

Standard form is written as $A \times 10^n$, where $1 \leq A < 10$. When moving the decimal point to the left, the exponent increases; when moving it to the right, the exponent decreases.

3. Show the solution

Step 1: Convert all terms to $10^{-5}$

• Term 1: $16.54 \times 10^{-5}$ (Already in $10^{-5}$)
• Term 2: $6.76 \times 10^{-8}$ To change $10^{-8}$ to $10^{-5}$, we move the decimal point 3 places to the left: $6.76 \times 10^{-8} = 0.00676 \times 10^{-5}$
• Term 3: $0.23 \times 10^{-6}$ To change $10^{-6}$ to $10^{-5}$, we move the decimal point 1 place to the left: $0.23 \times 10^{-6} = 0.023 \times 10^{-5}$

Step 2: Perform the arithmetic Now, combine the coefficients: $(16.54 - 0.00676 + 0.023) \times 10^{-5}$

• $16.54 - 0.00676 = 16.53324$
• $16.53324 + 0.023 = 16.55624$

So, we have: $16.55624 \times 10^{-5}$

Step 3: Convert to proper standard form Standard form requires the decimal to be after the first non-zero digit: $16.55624 \times 10^{-5} = 1.655624 \times 10^{-4}$

Rounding this to two decimal places (as seen in the options): $1.66 \times 10^{-4}$

4. Identify the answer

Comparing our result to the options provided, it matches option A.

5. Tip

When dealing with addition or subtraction of numbers in standard form, always convert them to the highest exponent present in the expression. This keeps your numbers as decimals rather than very small fractions, making them much easier to manage without a calculator.