Question

sy

求解11

11 已知log2~0.3010,log3~0.4771,log7≈0.8451。問:
44(1)12 是幾位數?
Eres
1000
(2)將0.98 表示成小數時,從小數點後第幾位開始出現不為0的數字?
gd l
40
解(1) 2
= (10 10912) 40
apak - Dop
*Pak

Answer 1

✨ 最佳解答 ✨

qn

log(12⁴⁰)=40 log12
=40(log4+log3)
=40(2log2+log3)
≈40(2×0.3010+0.4771)
=40×(0.6020+0.4771)
=40×1.0791
=43.164
所以 12⁴⁰≈10⁴³•¹⁶⁴ 為44位數

log(0.98¹⁰⁰⁰)
=1000 log(0.98)
=1000(log98-log100)
=1000(log2+log49-2)
=1000(log2+2log7-2)
≈1000(0.3010+2×0.8451-2)
=1000(0.3010+1.6902-2)
=1000×(1.9912-2)
=1000×(-0.0088)
=-8.8
所以 0.98¹⁰⁰⁰≈10⁻⁸•⁸=(10⁰•²)×10⁻⁹
故從小數點後第9位開始出現不為0的數字