GCSE Edexcel Maths Transformations: 7 (a) Write the number 0.0000862

7 (a) Write the number 0.00008623 in standard form - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 2

Question 8

7 (a) Write the number 0.00008623 in standard form. (b) Work out $$\frac{3.2 \times 10^{10} + 5.1 \times 10^{-2}}{4.3 \times 10^{4}}$$ Give your answer in standar... show full transcript

Worked Solution & Example Answer:7 (a) Write the number 0.00008623 in standard form - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 2

Step 1

Write the number 0.00008623 in standard form.

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Answer

The number 0.00008623 can be expressed in standard form as follows:

Firstly, we identify the significant digits, which in this case are 8623. We need to represent this in the form of $a \times 10^n$ where $1 \leq a < 10$ .

The significant digits 8623 can be written as: $8.623 \times 10^{-5}$

Thus, the number 0.00008623 in standard form is:

$8.623 \times 10^{-5}$ .

Step 2

Work out $$\frac{3.2 \times 10^{10} + 5.1 \times 10^{-2}}{4.3 \times 10^{4}}$$

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Answer

To solve the expression, we first compute the numerator and then the entire fraction.

Step 1: Compute the numerator

We need to handle $3.2 \times 10^{10} + 5.1 \times 10^{-2}$ . Since these terms have different exponents, we will convert them to have the same exponent before adding:

Converting $5.1 \times 10^{-2}$ to the same exponent as $10^{10}$ : $5.1 \times 10^{-2} = 5.1 \times 10^{-2} \times \frac{10^{10}}{10^{10}} = 5.1 \times 10^{8}$

Adding these values: $3.2 \times 10^{10} + 5.1 \times 10^{8} = 3.2000000000 \times 10^{10} + 0.000000051 \times 10^{10}$ $= (3.200000051) \times 10^{10}$

Step 2: Compute the entire expression

Now, substituting this back, we have: $\frac{(3.200000051) \times 10^{10}}{4.3 \times 10^{4}}$

Next, we simplify: $= (3.200000051 / 4.3) \times 10^{(10-4)}$ $= 0.744186 imes 10^{6}$

Step 3: Convert to standard form

To express this in standard form, we can write: $7.44186 \times 10^{5}$

When rounded to three significant figures, the final answer is:

$7.44 \times 10^{5}$ .