Question

by cindy grigg
1 we use numbers to measure many things. common numbers are used to measure the common things we see every day. the common way we write numbers is called standard notation. when we need to measure something that is very, very big or very, very small, we can use scientific notation. it is a shortcut for writing very big and very small numbers.
2 a number written in scientific notation is written as the product of a number between one and ten and a power or exponent of ten. here’s an example. you could write a distance of 2,000 miles as 2.0 × 10³ miles. it is read as “two times ten to the third power.” ten to the third power (10³) means 10 × 10 × 10. when you multiply a whole number by ten with any exponent, you move the decimal point to the right for every number in the exponent. ten to the third power means that you move the decimal point three places to the right. just add zeroes if you need to.
3 small numbers that are written with negative exponents. a negative exponent tells you that the decimal point is moved that number of places to the left. for example, five cents is written as $0.05. you could write it in scientific notation as 5.0 × 10⁻² dollars.
4 scientific notation is a simpler and shorter way to write really large or really small numbers. you just have to know the secret! numbers with positive exponents will be large and the zeroes will be added to the right. numbers with negative exponents will be small. the zeroes will be added to the left of the first number.

1. what number is most likely to be written in scientific notation?

a your weight
b the distance from the sun to saturn
c the distance from your house to your school
d your speed on a bicycle

1. what is 4.0 × 10² written in standard notation?

a 40,000
b 4,000,000
c 400
d 400,000

1. a number written in scientific notation with a negative exponent will be ______.

a a large number
b a small number
c a negative number
d none of the above

1. what is the correct way to write 3 million (3,000,000) in scientific notation?

a .03 × 10⁸
b 3.0 × 10⁶
c 3000 × 10³
d 30.0 × 10⁵

1. write 0.01 in scientific notation.

1. the distance from the sun to mars is about 141,000,000 miles. write that number using scientific notation.

Explanation:

Question 1

Scientific notation is for very big/small numbers. Weight (A) is moderate, house - school distance (C) and bicycle speed (D) are also moderate. Distance from sun to Saturn (B) is very large, so it's most likely in scientific notation.

Step1: Recall scientific to standard conversion.

To convert \(4.0\times10^{2}\) to standard, we move the decimal 2 places right (since exponent is 2).

Step2: Perform the conversion.

\(4.0\times10^{2}=4.0\times100 = 400\)

From the text, negative exponents mean decimal moves left (small numbers). So a number in scientific notation with negative exponent is a small number.

Answer:

B. The distance from the sun to Saturn

Question 2