Sure, let's solve these step-by-step:
### Part (a)
To convert the number [tex]\(1.89 \times 10^{-6}\)[/tex] to a decimal:
1. The exponent [tex]\(-6\)[/tex] indicates that we need to move the decimal point 6 places to the left.
2. Starting with the number [tex]\(1.89\)[/tex], we will move the decimal 6 places to the left, which means adding zeros in front of the number.
So:
[tex]\[
1.89 \times 10^{-6} = 0.00000189
\][/tex]
Therefore:
[tex]\[
1.89 \times 10^{-6} = 0.00000189
\][/tex]
### Part (b)
To write the number [tex]\(648,000\)[/tex] in scientific notation:
1. Identify where the decimal point currently is in the number. For [tex]\(648,000\)[/tex], it's implicitly at the end (648,000.).
2. Move the decimal point to a position where only one non-zero digit remains to its left. For [tex]\(648,000\)[/tex], moving the decimal point 5 places to the left, we get [tex]\(6.48\)[/tex].
3. Count the number of places the decimal point was moved. In this case, it was moved 5 places.
So:
[tex]\[
648,000 = 6.48 \times 10^5
\][/tex]
Therefore:
[tex]\[
648,000 = 6.48 \times 10^5
\][/tex]
#### Summary:
- Part (a): [tex]\(1.89 \times 10^{-6} = 0.00000189\)[/tex]
- Part (b): [tex]\(648,000 = 6.48 \times 10^5\)[/tex]
