Scientific and Standard Notation

​Scientific Notation and Standard Notation

By Ferdad Roidad

Standard Notation

Standard Notation is the "usual" way of writing numbers

• Standard notation is the "usual" way of writing numbers with digits from 0 to 9 and including commas as thousand separators and a period as a decimal point.

• If a decimal point is not displayed for a given number, then the decimal point is understood to follow the last digit of the number. For example, 623 is 623.0

• Alternatives to standard notation are word form and expanded form.

• A word form example is "one thousand" and an expanded form example is 600+20+3.
  

Scientific Notation

Scientific notation is an alternative to standard notation and writes a number as a product of a number and a power of 10. The number must be at least 1.0 and less than 10.0. The power of 10 may be positive, negative, or 0.

Scientific Notation

a number multiplied by a power of 10, such that the number is at least 1.0 and less than 10.0 and the power of 10 can be 0, positive, or negative.

Multiple Choice

$$10^0=$$

Hint: $$x^0=1$$ for all nonzero real numbers.

• $$0$$

• $$1$$

• $$10$$

• $$-1$$

• $$\frac{1}{10}or\ 0.1$$

Multiple Choice

$$10^{-1}=$$

Hint: $$x^{-1}=\frac{1}{x}$$ , negative one as an exponent results in the reciprocal of the base value.

• $$-0.1\ or-\frac{1}{10}$$

• $$0$$

• $$\frac{1}{10}\ or\ 0.1$$

• $$-10$$

Multiple Choice

$$10^{-2}=$$

Hint: $$x^{-2}=\frac{1}{x^2}$$ , negative two as an exponent results in the reciprocal of the base value squared.

• $$-100$$

• $$-\frac{1}{100}or-0.01$$

• $$\frac{1}{100}or\ 0.01$$

• $$100$$

• $$-20$$

Multiple Choice

The standard form value $$0.99$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$9.9\times10^1$$

• $$0.99\times10^0$$

• $$9.9\times10^0$$

• $$9.9\times10^{-1}$$

• $$0.99\times10^1$$

Multiple Choice

The standard form value $$0.1$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$1.0\times10^1$$

• $$1.0\times10^0$$

• $$1.0\times10^{-1}$$

• $$0.1\times10^1$$

• $$10.0\times10^{-2}$$

Multiple Choice

The standard form value $$0.01$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$1.0\times10^{-1}$$

• $$1.0\times10^{-2}$$

• $$0.1\times10^{-1}$$

• $$0.01\times10^{-2}$$

• $$10.0\times10^{-4}$$

Multiple Choice

The standard form value $$10$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$10.0\times10^0$$

• $$10.0\times10^1$$

• $$10.0\times10^{-1}$$

• $$1.0\times10^0$$

• $$1.0\times10^1$$

Multiple Choice

The standard form value $$100.001$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$1.0\times10^2$$

• $$1.00001\times10^2$$

• $$1.00001\times10^{-2}$$

• $$1.0\times10^{-2}$$

• $$10.001\times10^1$$

Multiple Choice

The standard form value $$0.31415$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$0.31415\times10^1$$

• $$0.31415\times10^{-1}$$

• $$3.1415\times10^0$$

• $$3.1415\times10^{-1}$$

• $$31.415\times10^{-2}$$

Multiple Choice

Given the standard form value 78,000,000 which is 78 million in word form, what is the scientific notation form?

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$78\times10^6$$

• $$7.8\times10^6$$

• $$7.8\times10^7$$

• $$0.78\times10^8$$

• $$78\times10^7$$

Fill in the Blanks

Given the scientific notation value $7.05\times10^3$ , what is the standard notation value?

Hint: Multiplying a number by a positive power of 10 increases the number's value, so we move the decimal point to the right and in this case, the decimal point is moved 3 digits to the right. You should get a whole number value.

Multiple Choice

The standard form value $$0.0003$$ in scientific notation is:

Hint: Scientific notation involves a number multiplied by a power of 10. The number must be at least $$1$$ and less than $$10$$ .

• $$0.3\times10^{-3}$$

• $$3.0\times10^{-3}$$

• $$3.0\times10^4$$

• $$3.0\times10^{-4}$$

• $$0.3\times10^{-4}$$

Multiple Choice

Given the scientific notation value $$9.0\times10^{-1}$$ , what is the standard notation value?

Hint: Multiplying a number by a negative power of 10 decreases the value of that number which means we move the decimal point to the left 1 digit in this case.

• $$-9$$

• $$90$$

• $$9$$

• $$-0.9$$

• $$0.9$$

Multiple Choice

What is the standard notation form for the given scientific notation value?

$$6.08\times10^{-1}$$

Hint: Multiplying a number by a negative power of 10 decreases the value of that number which means we move the decimal point to the left 1 digit in this case.

• $$-60.8$$

• $$-6.08$$

• $$60.8$$

• $$0.608$$

• $$-0.608$$

Multiple Choice

What is the standard notation form for the given scientific notation value?

$$6.08\times10^2$$

Hint: Multiplying a number by a positive power of 10 increases the value of that number which means we move the decimal point to the right 2 digits in this case.

• $$0.0608$$

• $$608$$

• $$0.608$$

• $$-608$$

• $$60800$$