Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Write In Standard Form

Write (3 + 2) • (1/10) + 4 • (1/1000) in standard form.

I think by standard form it is asking for the decimal interpretation.

Let me see.

(3 + 2) • (1/10) + 4 • (1/1000)

PEMDAS works here. 

(3 + 2) • (1/10) + 4 • (1/1000)

5 • (1/10) + 4 •(1/1000)

(1/2) + 4 • (1/1000)

(1/2) + (1/250) = (63/125).

In decimal form, (63/125) is
0.504.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Write In Standard Form

hi harpazo1965

See https://www.bbc.co.uk/bitesize/guides/z … revision/1

Your arithmetic is correct but it is best to leave the powers of ten if you want to end up with standard (index) form.

So a number between 1 and 10 followed by a power of ten.

Back in the days before calculators logarithm tables were often used to do calculations.  A table book usually had the logs of numbers between 1 and 10 so having numbers in stardard form made this easier.

eg.  In base ten log 2 ≈ 0.3010 ; log 20 = 1.3010 ; log 200 ≈ 2.3010 ; log 0.2 ≈ -1 + 0.3010 ; log 0.02 ≈ -2 + 0.3010 etc.

Page 6 of that BBC bitesize shows a calculation using standard form and page 7 shows how a calculator displays numbers that are too big |(or small) to fit the screen size.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Write In Standard Form

Hi Bob.

Thank you for your reply. I agree with what you said about standard (index) form. However, this question was texted to me by one of my brothers whose 5th grader got stuck with not only the calculation part but also not understanding the meaning of standard form. Children in 5th grade do not write their answer in scientific notation. I think it's best just to leave the answer as a decimal. You say?

Also, it is my hope to get a reply to my threads by different mathematicians, tutors, teachers, professors, etc. I thank you for taking time out to help me. It's very kind and professional of you to do so. I would like to see more participation from other members as well. Anyway, I better get some sleep. I gotta return to work tonight.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Write In Standard Form

If the question asks for standard form then that's what is expected.  Half the question is the working out; the other half is having the answer in sf.  No getting away from it I'm afraid.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Write In Standard Form

In that case, my answer of 0.504 should be 5 x 10^(-1). Correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Write In Standard Form

5.04 x 10^(-1)

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Write In Standard Form

Thanks. I know that 5.04 is between 1 and 10 and perfectly logical to multiply  that decimal number by 10^(-1), which is 1/10. I will try imgur this weekend.